Theoretical study of topological gyrotropic lattices with dynamic long-range interactions

Abstract

Topological photonics have been of great interest for the past decade, as the topological edge modes were proven to be robust against local perturbations. In this thesis, we study one-dimensional (1D) topological gyrotropic lattices beyond the Su-Schrieffer-Heeger (SSH) model. Different from the conventional SSH model that has only nearest-neighbor interactions, we consider, in general, dispersive systems with dynamic long-range interactions. The electromagnetic resonances of both gyroelectric lattices and gyromagnetic lattices are studied and compared. We find that the normal modes of the system coupled strongly to the photon mode of the background medium. In particular, the dynamic effects create a different band gap in gyromagnetic systems. We propose a 1D topological model for such a dispersive gyromagnetic system and demonstrate that the dynamic long-range interaction can lead to localized topological edge modes, while the quasi-static interaction alone does not. Our results indicate that the dynamic long-range interaction plays a crucial role in predicting the precise band structures and the spectral position of the topological edge modes in strongly dispersive gyrotropic systems, which deepen our understanding on the topology in non-reciprocal photonics.